Multi-disciplinary ship synthesis models and multi-objective optimization techniques are increasingly being used in ship design. Multi-disciplinary models allow designers to break away from the traditional design spiral approach and focus on searching the design space for the best overall design instead of the best discipline-specific design. Complex design problems such as these often have high levels of uncertainty associated with them, and since most optimization algorithms tend to push solutions to constraint boundaries, the calculated "best" solution might be infeasible if there are minor uncertainties related to the model or problem definition. Consequently, there is a need to address uncertainty in optimization problems to produce effective and reliable results. This thesis focuses on adding a third objective, uncertainty, to the effectiveness and cost objectives already present in a multi-disciplinary ship synthesis model. Uncertainty is quantified using a "confidence of success" (CoS) calculation based on the mean value method. CoS is the probability that a design will satisfy all constraints and meet performance objectives. This work proves that the CoS concept can be applied to synthesis models to estimate uncertainty early in the design process. Multiple sources of uncertainty are realistically quantified and represented in the model in order to investigate their relative importance to the overall uncertainty. This work also presents methods to encourage a uniform distribution of points across the Pareto front. With a well defined front, designs can be selected and refined using a gradient based optimization algorithm to optimize a single objective while holding the others fixed.